y^2-6y-22=0

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Solution for y^2-6y-22=0 equation: 


Simplifying
y2 + -6y + -22 = 0

Reorder the terms:
-22 + -6y + y2 = 0

Solving
-22 + -6y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -6y + 22 + y2 = 0 + 22

Reorder the terms:
-22 + 22 + -6y + y2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -6y + y2 = 0 + 22
-6y + y2 = 0 + 22

Combine like terms: 0 + 22 = 22
-6y + y2 = 22

The y term is -6y.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6y + 9 + y2 = 22 + 9

Reorder the terms:
9 + -6y + y2 = 22 + 9

Combine like terms: 22 + 9 = 31
9 + -6y + y2 = 31

Factor a perfect square on the left side:
(y + -3)(y + -3) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(y + -3) equal to 5.567764363 and -5.567764363.


Subproblem 1
y + -3 = 5.567764363

Simplifying
y + -3 = 5.567764363

Reorder the terms:
-3 + y = 5.567764363

Solving
-3 + y = 5.567764363

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + y = 5.567764363 + 3

Combine like terms: -3 + 3 = 0
0 + y = 5.567764363 + 3
y = 5.567764363 + 3

Combine like terms: 5.567764363 + 3 = 8.567764363
y = 8.567764363

Simplifying
y = 8.567764363


Subproblem 2
y + -3 = -5.567764363

Simplifying
y + -3 = -5.567764363

Reorder the terms:
-3 + y = -5.567764363

Solving
-3 + y = -5.567764363

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + y = -5.567764363 + 3

Combine like terms: -3 + 3 = 0
0 + y = -5.567764363 + 3
y = -5.567764363 + 3

Combine like terms: -5.567764363 + 3 = -2.567764363
y = -2.567764363

Simplifying
y = -2.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.567764363, -2.567764363}

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